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This paper presents the mass assembly time scales of nearby galaxies observedby CALIFA at the 3.5m telescope in Calar Alto. We apply the fossil recordmethod of the stellar populations to the complete sample of the 3rd CALIFA datarelease, with a total of 661 galaxies, covering stellar masses from 10$^{8.4}$to 10$^{12}$ M$_{\odot}$ and a wide range of Hubble types. We apply spectralsynthesis techniques to the datacubes and process the results to produce themass growth time scales and mass weighted ages, from which we obtain temporaland spatially resolved information in seven bins of galaxy morphology and sixbins of stellar mass (M$_{\star}$) and stellar mass surface density($\Sigma_{\star}$). We use three different tracers of the spatially resolvedstar formation history (mass assembly curves, ratio of half mass to half lightradii, and mass-weighted age gradients) to test if galaxies grow inside-out,and its dependence with galaxy stellar mass, $\Sigma_{\star}$, and morphology.Our main results are as follows: (a) The innermost regions of galaxies assembletheir mass at an earlier time than regions located in the outer parts; thishappens at any given M$_{\star}$, $\Sigma_{\star}$, or Hubble type, includingthe lowest mass systems. (b) Galaxies present a significant diversity in theircharacteristic formation epochs for lower-mass systems. This diversity shows astrong dependence of the mass assembly time scales on $\Sigma_{\star}$ andHubble type in the lower-mass range (10$^{8.4}$ to 10$^{10.4}$), but a verymild dependence in higher-mass bins. (c) All galaxies show negative$\langle$log age$\rangle_{M}$ gradients in the inner 1 HLR. The profileflattens with increasing values of $\Sigma_{\star}$. There is no significantdependence on M$_{\star}$ within a particular $\Sigma_{\star}$ bin, except forthe lowest bin, where the gradients becomes steeper.

The spatially resolved star formation history of CALIFA galaxies: Cosmic time scales